1. Parallel programming laboratory

2. Iterated function attractors
z = x + iy
Converge into point p
Divergent
Evolve in a closed region: Attractor

3. z  z2 z = r e i r  r 2   2 divergent convergent 1
Attractor: H = F(H)

4. Attractor
The attractor is a boundary between the divergent and convergent region
Filled attractor = non divergent region
z n+1 = z n2 : if |z |<  then black

5. Julia set: z  z2 + c

6. Filled Julia set: algorithm
Im z
(X,Y)
FilledJuliaDraw ( )
FOR Y = 0 TO Ymax DO
FOR X = 0 TO Xmax DO
ViewportWindow(X,Y  x, y)
z = x + j y
FOR i = 0 TO n DO z = z2 + c
IF |z| > “infinity” THEN WRITE(X,Y, white)
ELSE WRITE(X,Y, black)
ENDFOR
END
Re z

7. Mandelbrot set Those C complex numbers, where the
z  z2 + c Julia set is connected

8. Mandelbrot set, algorithm
MandelbrotDraw ( )
FOR Y = 0 TO Ymax DO
FOR X = 0 TO Xmax DO
ViewportWindow(X,Y  x, y)
c = x + j y
z = 0
FOR i = 0 TO n DO z = z2 + c
IF |z| > “infinity” THEN WRITE(X,Y, white)
ELSE WRITE(X,Y, black)
ENDFOR
END